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TIME OF DAY CORRELATIONS FOR IMPROVED WIND SPEED PREDICTIONS ANDREW OLIVER, PhD KRISTOFER ZARLING VP TECHNOLOGIES WIND DATA ANALYST 7TH MAY 2009 1
WHY THE NEED? • Diurnal wind speed profile is often very different at lower versus higher levels • Atmospheric stability effects on wind speed at two levels on the same tower • Consequently the relationship between Site and Reference station often varies with Time Of Day • An MCP process that fails to take account of Time Of Day is likely to be deficient for many sites Ratio = 1.61 Ratio = 1.20 Many, if not most, long term reference stations (airports, etc) used in M.C.P. analysis (wind speed predictions) measure close to the ground (around 10 m.)
AN EXAMPLE: DIRECTIONAL RATIOS AND TIME OF DAY RATIOS • Binning by DIRECTION 12 sectors (of 30°) wind speed ratio ranges from 1.35 to 1.92 • Binning by TIME 12 sectors (of 2 hours) wind speed ratio ranges from 1.21 to 1.98 • Standard Deviation of ratios much greater for TIME than for DIRECTION • Number of counts is few for some DIRECTIONS. TIME sectors have equal counts Standard Deviation 0.19 Standard Deviation 0.32 Ratio of means analysis for a ‘typical’ Texas site
A STATEMENT AND A QUESTION STATEMENT “It seems obvious that better relationships between a site and a reference station can be obtained for SOME SITES by taking a TIME sectoring approach as opposed to a DIRECTION sectoring approach. Particularly where the terrain is less complex and atmospheric stability varies significantly on a diurnal basis.” QUESTION “Can it lead to better predictions though?”
A TEST CASE • CORRELATE 1 YEAR OF DATA WITH A NEARBY REFERENCE STATION • First binned the data into the following: • Formed 12 “Least-squares” regressions (Site versus Reference station). • Note: This was just a test. We do not recommend the use of least-squares for MCP!!! • “Back Predicted” Site wind speed using regressions formed & Reference station data • Determined regression coefficient of “Back Predictions” • How well did the regressions describe the relationship between Site and Reference?
CORRELATIONS IMPROVED WHEN “TIME” WAS INTRODUCED 12 TIME ‘SECTORS’ PRODUCED A BETTER ‘BACK PREDICTION’ THAN 12 DIRECTION SECTORS FOR THIS SITE ‘BACK PREDICTION’ IMPROVED FURTHER WHEN A COMBINATION OF DIRECTION AND TIME WAS USED
A STEP FURTHER FURTHER IMPROVEMENT WAS MARGINAL WITH MORE (24), AND VARIABLE WIDTH, TIME AND DIRECTION SECTORS
? SO WHAT NEXT?
PREDICTION METHODOLOGIES (NON EXHAUSTIVE) 1 (no binning) 12 Are You Crazy? Some combination of m Direction sectors and n Time sectors 40 ways of predicting wind speed in this non-exhaustive list! 4 ways were compared in this study
GATHERING THE DATA & PREDICTING • Selected 19 sites where RES Americas had collected at least 2 years of data • Good data availability (All >95%) • Geographically dispersed • Meteorologically varied • Use one year to predict another year. Two Ways: • Sliced: 2nd Year Predicts 1st Year & Vice Versa • Akin to what happens in the “real world” • Diced: Every even day Predicts every Odd Day & Vice Versa • Removes annual trending biases (if any) Year 1 Year 2 Site Regression Reference Station Time Odd Day Even Day
GATHERING THE DATA & PREDICTING, continued • A 6 month subset was also used to establish the relationship between Site & Reference • Tested ability of prediction method to account for seasonality • The total number of predictions carried out was: 19 Sites * 4 Regression methods * 2 Ways (Sliced & Diced) * 2 Years (Use 1st Year to predict 2nd Year & Vice Versa) * 2 Concurrent data lengths (1 Year and 6 months of data) • 608 Total • For the Direction / Time Combination method the following sectoring was used: • 6 Direction Sectors (1st centered on North) and 2 Time Sectors (6:00am to 6:00pm) • No “finesse” about how the hours, or directions were selected
RESULTS YEAR “SLICED” In all cases, the r value (weighted by sector counts) was greatest for the “12 Time” sector regressions
RESULTS cont. • Mean Absolute Error • “6 Direction & 2 Time” gave the lowest Mean Absolute Error in each case tested: • No significant differences in distributions of errors were observed • Direction is obviously still important. Mixed results compared with Time only • Not a huge improvement, but “6 Direction / 2 Time” was chosen arbitrarily • Simply keeping 12 directions and dividing the data into ‘day’ and ‘night’ could yield improved results without leaving too few data points for regression (50% reduced)
RESULTS cont. • Head to head: Direction versus Combination method (which is best?) • If we cannot a priori figure out which method to use then using 6 Direction and 2 Time sectors produces a better result than 12 Direction sectors in the majority of cases!!! • An important result
CONCLUSIONS • Time of Day has been introduced as a binning parameter in MCP as a proxy for atmospheric stability • Time of Day is an important factor to consider in MCP • Regression coefficients were improved in 100% of ‘Year Sliced’ test cases (12 Time Sectors versus 12 Direction Sectors). 95% for ‘6 Months Sliced’ • Choosing 6 Direction sectors and 2 Time sectors instead of the traditional 12 Direction approach produced a better prediction in the majority of cases • This choice was fairly arbitrary. It is postulated that varying Time and Direction sector widths on a case by case basis will yield improved results • It is further postulated that keeping the traditional 12 Direction Sectors, but adding 2 Time Sectors (for a total of 24 sectors) will also improve predictions while still retaining enough data points in each sector (50% reduced)
FUTURE WORK • Understand how to optimize the binning of data into m Direction and n Time sectors • Ideal problem for Neural Networks? • Understand Energy Bias errors (how well is the wind speed distribution is predicted) • But the wider question and the “Holy Grail” for MCP is still: • Which regression method should I use for a given site in order to minimize my error? • And the most important consideration (often overlooked) is that one has to have a decent long term reference station in the first place!
THANK YOU ANDREW OLIVER, PhD KRISTOFER ZARLING VP TECHNOLOGIES WIND DATA ANALYST RES AMERICAS, INC. 11101 West 120th Avenue, Suite 400 BROOMFIELD, CO 80021 (303) 439 4200 With thanks to Mike Anderson, Jerry Bass, Rajan Arora, Alex Kapetanovic & Karen-Anne Hutton